9-1 Developing Formulas for Triangles and Quadrilaterals Warm Up Lesson Presentation Lesson Quiz Holt Geometry

Warm Up Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = 21 2. b = 21, c = 35 3. a = 20, c = 52 c = 29 a = 28 b = 48

Objectives Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles and special quadrilaterals.

Steps (IMPORTANT – Do all of these steps on homework and the test for full credit!!): Write out formula Substitute in known values Solve for desired value

Area of the rectangle is A= b(h) The perimeter of a rectangle with base b and h is P = 2b + 2h or P = 2 (b + h). Remember! Area of the rectangle is A= b(h)

The height of a parallelogram is measured along a segment perpendicular to a line containing the base. Remember! Check out: http://www.keymath.com/x3338.xml to learn about the area formula of a parallelogram.

To find the area formula for a trapezoid, visit: http://www.geogebra.org/en/upload/files/english/Barbara_Perez/Area_Trapezoid.html

Example 2A: Finding Measurements of Triangles and Trapezoids Find the area of a trapezoid in which b1 = 8 in., b2 = 5 in., and h = 6.2 in. Area of a trapezoid Substitute 8 for b1, 5 for b2, and 6.2 for h. A = 40.3 in2 Simplify.

Example 2C: Finding Measurements of Triangles and Trapezoids Find b2 of the trapezoid, in which A = 231 mm2. Area of a trapezoid Substitute 231 for A, 23 for , and 11 for h. Multiply both sides by . 42 = 23 + b2 19 = b2 Subtract 23 from both sides. b2 = 19 mm Sym. Prop. of = http://www.geogebra.org/en/upload/files/english/Barbara_Perez/Area_Trapezoid_Practice.html

The diagonals of a rhombus or kite are perpendicular, and the diagonals of a rhombus bisect each other. Remember! http://www.geogebra.org/en/upload/files/english/Barbara_Perez/Area_Kite.html http://www.geogebra.org/en/upload/files/english/Barbara_Perez/Area_Rhombus.html

Example 3A: Finding Measurements of Rhombuses and Kites Find d2 of a kite in which d1 = 14 in. and A = 238 in2. Area of a kite Substitute 238 for A and 14 for d1. 34 = d2 Solve for d2. d2 = 34 Sym. Prop. of = http://www.geogebra.org/en/upload/files/english/Barbara_Perez/Area_Kite_Practice.html